As of 2012 the states or regions where SC residents were born:
58% born in SC
7% born in other Northeastern states (non-NY)
7% born in other Southern states
6% born in the Midwest
6% born outside the United States
4% born in NY
3% born in GA
3% born in Western states
So 7% of SC residents were born in other Southern states - including TX. I suspect the reason is, people are looking at distance to relatives and friends when they move as well as factors like jobs. I know that for years I've heard people here in the Midwest who moved to FL tend to go to the west coast of the state, but people from the Northeast tend to go to the east coast of the state.
Source:
https://www.nytimes.com/interactive/...were-born.html
Note the widget above each graph that lets you switch from a display of migration out vs. migration into each state.